Sierpinski / Riesel - Base 22

Conjectured Sierpinski at 6694 [5,23,97]

Conjectured Riesel at Riesel 4461 [5,23,97]

Pesky 17 k's include (now 13 to go)

Sierpinski:

22 (cedricvonck)

484 (cedricvonck)

1611 (michaf tested upto 12000)

1908 (michaf tested upto 12000)

4233 (michaf tested upto 12000)

5128 (michaf tested upto 12000)

5659 (michaf tested upto 12000)

6462 (michaf tested upto 12000)

Riesel:

1013 (michaf tested upto 12000)

2853 (michaf tested upto 12000)

3104 (michaf tested upto 12000)

3656 (michaf tested upto 12000)

4001 (michaf tested upto 12000)

22 and 484 are special cases; only non-trivials occur with n=2^m

If a prime is found for 22 case, 484 is also eliminated (n is one lower in that case)

(larger) primes found:

4118*22^12347-1 (michaf)

6234*22^16010+1 (michaf)

942*22^18359+1 (michaf)

5061*22^24048+1 (michaf)

22*22^n+1 / 484*22^n+1 status:

Code:

below (512): proven composite with phrot
(512) 22^512+1 has factor 115443366400367617
(1k) 22^1024+1 has factor 2095383775764481
(2k) 22^2048+1 has factor 65465822271579614082713282973697
(4k) 22^4096+1 has factor 40961
(8k) 22^8192+1 has factor 147457
(16k) 22^16384+1 has factor 2342241402881
(32k) 22^32768+1 has factor 65537
(64k) 22^65536+1 has factor 27918337
(128k) 22^131072+1 has factor 786433
(256k) 22^262144+1 has factor 29884417
(512k) 22^524288+1 has factor 93067411457
**(1M)** no factors upto 1607651162167705601 (also P-1 stage 1 done with B1=100000 and 25 ECM curves, B1=1000, B2=100000)
**(2M)** no factors upto 285159626880581633
**(4M)** no factors upto 556968483053633537
**(8M)** no factors upto 9221584136710389761 (stopping here)
(16M) 22^16777216+1 has factor 189162539974657
(32M) 22^33554432+1 has factor 21096518178045953
**(64M)** no factor upto 9202942106325221377 (stopping here)
(128M) 22^134217728+1 has factor 91268055041
(256M) 22^268435456+1 has factor 7368180622415626241
**(512M)** no factor upto 9187751282130026497 (stopping here)
**(1G)** no factor upto 9159662798383349761 (stopping here)